Over time, it has become increasingly useful and necessary to enhance the accuracy of the measurement of a quantity, such as, for example, distance.
Interferometry now provides a convenient and highly sensitive method for measuring a quantity, such as distance, optically. For some applications, such as, for example, those which relate a common distance measured by two radiations of differing wavelength, it may be optimally effective to make the measurements in vacuum to obtain a wavelength ratio as accurately as possible. For other measurement situations, however, where, for example, the objective is to establish a physical distance, it is clearly more attractive to measure the distance in the ambient atmosphere rather than in vacuum.
Apparatus is commercially available offering intrinsic fringe-counting measurement capability in vacuum with inaccuracies in the range of one part in 10.sup.8. To achieve such accuracy in an ambient atmosphere, such as, for example, in the attractive case of interferometry in air, the measured length would have to be corrected for the refractive index of the atmosphere, a factor somewhat greater than unity, and dependent upon the gaseous composition, temperature, pressure, humidity, and the like.
In years of careful work, B. Edlen developed an empirical expression for the index of refraction (B. Edlen, "The Refractive Index of Air", Metrologia 2, 71-80 (1966)) based upon data of H. Barrell and J.E. Sears Jr. (Philosophical Transactions of the Royal Society of London, Series A, 238 p. 1 (1939)). Many others have extended this analysis to better represent the density dependence using local field corrections and virial expansions, for example. More recently, an international collaboration of experts has recommended the following approximate formula for the index of refraction (n) of standard air near usual laboratory conditions: ##EQU1## with D=0.27651756.times.10.sup.-3 [1+54.times.10.sup.-8 (C-300)], where P is the pressure in Pa, T is the temperature in degrees centigrade, F is the partial pressure of water vapor in Pa, and C is the CO.sub.2 concentration in ppm. The formula set forth above represents the index of refraction at the wavelength of the 633 nm HeNe laser (632.991 398 nm in vacuum).
It can be seen that the correction due to atmospheric refractivity amounts to 270 parts per million at sea level. Thus, to reach an inaccuracy of 1 part in 10.sup.8, it is necessary to know the refractivity at the level of 1 part in 27,000. One way to reduce this sensitivity is to employ a balanced-path interferometer. For many applications, however, it is necessary, or at least more desirable, to measure through an unbalanced distance interval of about one meter due to several technical reasons. Furthermore, making the apparatus single-ended allows the heat-generating laser apparatus to be located somewhat away from the sensitive area where it is desired to make the actual measurement. The result is that the interferometric length measurement accuracy is often unacceptably compromised by inaccurate knowledge of the atmospheric index of refraction.
One possibility for the in-situ determination of the atmospheric index of refraction would be to individually measure (or estimate) the atmospheric pressure, temperature, humidity, and CO.sub.2 content. A measurement objective of even 0.1 ppm relative length accuracy, however, requires pressure and temperature measurement at the 0.02% level, viz. 0.2 millibar and 0.06 K. These values are several orders of magnitude beyond any practical known calibration of generic transducers and so must be obtained by painstakingly careful and expensive calibration relative to accurate working standards. Furthermore, the refractivity of water vapor is about 15% below that of dry air, so the relative humidity must be known to within 0.14% of absolute, which is not easy to achieve without direct measurement of the dew point. Finally, the environmental atmosphere is enriched beyond the usual 300 ppm level of CO.sub.2 concentration by the respiration of people working in the measurement area. A factor of 2 increase in the CO.sub.2 concentration is typical for a few hours work in a closed room. However, the refractivity of CO.sub.2 is approximately equal to (somewhat greater than) that of standard air so that changes in its concentration are only marginally significant at the 1:10.sup.7 level.
Prior art devices have addressed problems related to index of refraction measurements, but not for the purpose of quantifying the index of refraction of the surrounding atmosphere. For example, the use of Fabry-Perot etalons in vacuum to determine wavelength either with vidicon readout and analog processing (R.L. Byer, J. Paul and M.D. Duncan, "A Wavelength Meter", Laser Spectroscopy III, page 414 (1977)) or solid state detectors and digital processing (A. Fischer, R. Kullmer and W. Demtroder, "Computer Controlled Fabry-Perot Wavemeter", Optics Communications, 39, 277-282 (1981)) has heretofore been suggested. In addition, a technique for mapping a significant fraction of each Fabry-Perot ring into a corresponding spot (with an inherent loss of accuracy) has also been suggested (Hays, "Circle to Line Interferometer Optical System", Applied Optics, 29, 1482-1489 (1990)). The slight compression of Fabry-Perot etalons due to increases in atmospheric pressure has also been observed (M. Andersson, L. Eliasson and L.R. Pendrill, "Compressible Fabry-Perot Refractometer", Applied Optics, 26, 4835-4840 (1987)).
Previous patents also address related problems. U.S. Pat. No. 3,614,236 shows use of changes in the direction of the illumination of a Fabry-Perot interferometer caused by changes in atmospheric refractivity, to cancel changes in the interference condition caused by atmospheric pressure changes within the interferometer, with the apparatus including a HeNe laser and a plurality of optical units and detectors to count fringes. U.S. Pat. No. 4,329,058 shows a fiber optic sensor based on Fabry-Perot interferometry, and shows use of a plurality of charge coupled devices and a microprocessor having a decoding algorithm, with the device providing a means for measuring physical parameters at remote locations.
Thus, there is a need for a simple, robust system and method for determining the index of refraction of an ambient atmosphere, such as air, during the quantity measurement (such as measurement of distance, or length), for example, during the "step and repeat" process of patterning integrated circuit wafers using photolithography. As this industry moves toward tracewidths far below 1 .mu.m, it will become necessary to be able to determine the index of refraction even better, toward the 1:10.sup.8 level.